Finite Group Databasebeta

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C4×Dic772 #27135355

order12352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic772

Splittings

SylowC193 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4D772
commutatorC4×C193C22×C4
FrattiniC2×C4C22×D193
FittingC4×C8×C193C2
socle, prime radicalC22×C193C2×D4
cosocleC2×C4×C193C23
hypercenterC4×C8D193
hypocenterC193C4×Q16
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

110 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 645);